Quantum information processing with hyperentangled photon states

We discuss quantum information processing with hyperentangled photon states - states entangled in multiple degrees of freedom. Using an additional entangled degree of freedom as an ancilla space, it has been shown that it is possible to perform efficient Bell-state measurements. We briefly review these results and present a novel deterministic quantum key distribution protocol based on Bell-state measurements of hyperentangled photons. In addition, we propose a scheme for a probabilistic controlled-not gate which operates with a 50 % success probability. We also show that despite its probabilistic nature, the controlled-not gate can be used for an efficient, nonlocal demonstration of the Deutsch algorithm using two separate photons.